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Chapter 1: Problem 622

Convert each fraction to a decimal. $$ -\frac{284}{25} $$

Short Answer

Expert verified
-11.36

Step by step solution

01

Understand the problem

The task requires converting the fraction \(-\frac{284}{25}\) into decimal form.
02

Perform the division

Divide the numerator (284) by the denominator (25) to find the decimal value. Since the fraction is negative, the result will also be negative. \(-\frac{284}{25} = -11.36\).
03

Write the decimal

After performing the division, the final result is \(-11.36\).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Understanding Fractions
Let's dive deeper into understanding fractions. A fraction consists of two numbers: a numerator (the top number) and a denominator (the bottom number). For example, in the fraction \(\frac{284}{25}\), 284 is the numerator and 25 is the denominator. Fractions represent parts of a whole. When we convert a fraction to a decimal, we're essentially dividing the numerator by the denominator.

Key points to remember about fractions:
  • Numerator: The number above the line in a fraction. It represents how many parts of the whole we're considering.
  • Denominator: The number below the line. It shows into how many parts the whole is divided.
  • Negative Fractions: If the fraction is negative, the decimal will also be negative.
Understanding these basics helps make the process of converting fractions to decimals much easier.
Decimals
Decimals are another way to represent fractions or parts of a whole. Converting fractions to decimals helps in many mathematical situations because decimals are often easier to work with than fractions.

In the decimal system, place value is key:
  • Each place to the right of the decimal point represents a power of ten, starting with tenths, then hundredths, thousandths, and so on.
For example, the decimal 11.36 can be broken down into:
  • 11 (whole number part)
  • .3 (three-tenths)
  • .06 (six-hundredths)
Hence, 11.36 means 11 units plus 0.3 (or 3 tenths) plus 0.06 (or 6 hundredths). Understanding how decimals work makes converting them from fractions much clearer.
The Process of Division in Fraction to Decimal Conversion
Understanding division is crucial when converting fractions to decimals. Division is the process of calculating how many times one number is contained within another.

Here is the step-by-step process using our example, \(\frac{284}{25}\):
  • Identify the Numerator and Denominator: Here, the numerator is 284 and the denominator is 25.
  • Perform the Division: Divide 284 by 25. This can be done using long division or a calculator.
  • Interpreting the Result: The division gives 11.36. Since our original fraction is negative, the result is \(-11.36\).
Understanding each step ensures you can accurately and confidently convert any fraction to a decimal.

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